The adjoining diagram shows the spectral ener | vedclass

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(D) According to the Stefan-Boltzmann law,the total energy radiated per unit area per unit time by a black body is proportional to the fourth power of

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$4$

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(D) According to the Stefan-Boltzmann law,the total energy radiated per unit area per unit time by a black body is proportional to the fourth power of its absolute temperature $(E \propto T^4)$.The area under the spectral energy density curve $E_\lambda$ versus $\lambda$ represents the total emissive power of the black body.Given the ratio of the areas under the curves is $\frac{A_1}{A_2} = 16 : 1$,where $A_1$ corresponds to temperature $T$ and $A_2$ corresponds to $2000 \ K$.Using the relation $\frac{A_1}{A_2} = \left(\frac{T}{2000}ight)^4$,we have:$16 = \left(\frac{T}{2000}ight)^4$Taking the fourth root on both sides:$2 = \frac{T}{2000}$$T = 2 	imes 2000 = 4000 \ K$.

The adjoining diagram shows the spectral energy density distribution $E_\lambda$ of a black body at two different temperatures. If the areas under the curves are in the ratio $16 : 1$,the value of temperature $T$ is ......... $K$. (in $,000$)

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